“Witness” (Capitol), the pop singer’s first LP in four years, debuted atop the Billboard chart, just as her previous two did — “Prism” in 2013 and “Teenage Dream” in 2010 — despite a rockier commercial rollout. While Ms. Perry has collected 14 Top 10 hits on the Billboard Hot 100 throughout her career, singles from “Witness” have struggled some, with “Swish Swish” sitting at No. 83 and “Bon Appétit” at No. 98 ahead of the album’s release.

Still, “Witness” sold 162,000 copies in its first week and was streamed another 19 million times for a total of 180,000 album equivalent units, according to Nielsen Music. Ms. Perry is just the second woman to top the album chart this year, after Halsey last week. (In its first week on most streaming services, Taylor Swift’s “1989” had 19 million streams, enough to put it at No. 31 on the album chart; some saw the timing of Ms. Swift’s belated digital release as an attempt to undermine Ms. Perry, a longtime rival.)

Also on the chart this week: Kendrick Lamar’s “Damn.” is No. 2; the alternative R&B singer SZA’s “Ctrl” debuts at No. 3, largely on the strength of 50 million streams; No. 4 is Lady Antebellum’s “Heart Break”; and Drake’s “More Life,” from March, is No. 5.

There are some albums missing from the rankings as well (depending on your definition of an “album”). Two digital-only compilations that were in the Top 10 last week have fallen off the chart entirely after Billboard changed its rules regarding multi-artist projects: While “Epic AF” and “Summer Latin Hits 2017” were essentially playlists meant to game the system, charting almost entirely based on streams of existing songs, most various artist compilations will now only be eligible to chart based on traditional album sales, Billboard said.

From now on, only compilations that have songs specifically recorded for that project — including soundtracks and cast recordings — will be allowed to count streams and individual song downloads toward its sales total.

A version of this article appears in print on , Section C, Page 3 of the New York edition with the headline: Katy Perry’s ‘Witness’ Tops Billboard Chart. Order Reprints | Today’s Paper | Subscribe